1. What is the Radius of Hemisphere Formula?

The formula calculates the radius of a hemisphere when given its curved surface area. The curved surface area represents the area of the dome-shaped part of the hemisphere.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of the hemisphere (meters)
• \( CSA \) — Curved surface area of the hemisphere (square meters)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the relationship between the curved surface area of a hemisphere and its radius, using the mathematical constant pi.

3. Importance of Radius Calculation

Details: Calculating the radius from curved surface area is essential in geometry, architecture, and engineering applications where hemispherical structures are involved.

4. Using the Calculator

Tips: Enter the curved surface area in square meters. The value must be valid (greater than 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between total surface area and curved surface area?
A: Curved surface area includes only the dome-shaped part, while total surface area includes both the curved surface and the circular base.

Q2: Can this formula be used for full spheres?
A: No, this formula is specific to hemispheres. For full spheres, the formula for radius from surface area is different.

Q3: What units should I use for the input?
A: The calculator expects square meters for area input, but you can use any consistent unit system as long as you interpret the result accordingly.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and using the standard value of pi.

Q5: What if I have the total surface area instead of curved surface area?
A: You would need to subtract the base area first, then use this formula: CSA = Total Surface Area - πr² (but since r is unknown, you'd need to solve differently).